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The technique of identifying Lagrangian Coherent Structures (LCSs) has emerged as a powerful tool for studying incompressible flows. Yet, the discrepancies arising from incompressibility assumptions often compromise the accuracy of LCSs constructed using Lagrangian particle methods. In this study, we introduce a modified framework to compute Finite-Time Lyapunov Exponents (FTLEs), addressing the misalignment between the fully incompressible assumption of LCS theory and the inherent incompressibility loss in simulations of particle methods. We begin by examining the correlation between the minimum and maximum FTLEs. By incorporating the deformation gradient and Cauchy-Green strain tensor which account for the time-advancing errors of incompressibility based on continuum theory, we enhance the computational accuracy of FTLEs. Moreover, we introduce the modified FTLE algorithm to the incompressible particle-in-cell (PIC) method for resolving free surface flows and fluid-structure interaction problems. Finally, numerical examples including the Tayler-Green vortices, water sloshing with baffles, an eccentric box sinking in water, and three-dimensional shear-driven cavity problems with high Reynolds numbers are tested to validate the effectiveness of the modified FTLE algorithm and the improved LCSs. These results demonstrate that the proposed modification scheme adeptly counteracts the errors caused by incompressibility loss, enabling accurate computation of FTLEs and detection of LCSs. [ABSTRACT FROM AUTHOR]

Patient-specific simulation of the fluid–structure interaction (FSI) problems in cardiovascular systems plays an increasingly important role in fundamental research and clinical applications. However, modeling such problems is challenging, as they often involve non-trivial structural deformation, morphing flow domains, and complex interfaces. In this paper, we develop an incompressible SPH-total Lagrangian SPH (ISPH-TLSPH) framework well-adapted to cardiovascular FSI simulations. The matrix-free iterative ISPH method is used to simulate the hemodynamics and the stabilized TLSPH is used to simulate the dynamics of blood vessels. We propose a novel FSI coupling strategy to couple the ISPH with TLSPH, conforming to strict interface matching conditions. Moreover, we accurately incorporate the lumped parameter (0D) models into the 3D SPH framework to simulate the physiological effects of downstream vascular beds. Lastly, graphics processing unit (GPU) parallelization techniques are implemented in our framework to improve efficiency. The developed framework is first validated by investigating the pulse wave propagation in straight vessels under different boundary conditions. Then the FSI processes in the blood vessel with stenosis and the patient-specific aorta are modeled and investigated. The simulation results show that our framework is effective and efficient for the simulations of patient-specific blood vessels. • A framework that couples the matrix-free iterative ISPH with TLSPH is developed. • A novel coupling strategy for fluid–structure interaction is proposed. • A 3D-0D coupled model is introduced to the SPH framework. • GPU parallelization is implemented for accelerating SPH computations. [ABSTRACT FROM AUTHOR]